Comparison of Galerkin, POD and Nonlinear-Normal-Modes Models for Nonlinear Vibrations of Circular Cylindrical Shells

M Amabili 1 Cyril Touzé 2 O Thomas 3
1 Department of Mechanical Engineering [Montréal]
2 UME - Unité de Mécanique
3 LMSSC - Laboratoire de Mécanique des Structures et des Systèmes Couplés
Abstract : The aim of the present paper is to compare two different methods available to reduce the complicated dynamics exhibited by large amplitude, geometrically nonlinear vibrations of a thin shell. The two methods are: the proper orthogonal decomposition (POD) and an asymptotic approximation of the Nonlinear Normal Modes (NNMs) of the system. The structure used to perform comparisons is a water-filled, simply supported circular cylindrical shell subjected to harmonic excitation in the spectral neighbourhood of the fundamental natural frequency. A reference solution is obtained by discretizing the Partial Differential Equations (PDEs) of motion with a Galerkin expansion containing 16 eigenmodes. The POD model is built by using responses computed with the Galerkin model; the NNM model is built by using the discretized equations of motion obtained with the Galerkin method, and taking into account also the transformation of damping terms. Both the POD and NNMs allow to reduce significantly the dimension of the original Galerkin model. The computed nonlinear responses are compared in order to verify the accuracy and the limits of these two methods. For vibration amplitudes equal to 1.5 times the shell thickness, the two methods give very close results to the original Galerkin model. By increasing the excitation and vibration amplitude, significant differences are observed and discussed.
Keywords : nonlinear normal modes POD shells nonlinear vibrations
Document type :
Conference papers
Complete list of metadatas

Cited literature [37 references]  Display  Hide  Download
https://hal-ensta-paris.archives-ouvertes.fr//hal-01154712
Contributor : Cyril Touzé <>
Submitted on : Wednesday, May 27, 2015 - 10:37:13 AM
Last modification on : Wednesday, July 3, 2019 - 10:48:04 AM
Long-term archiving on: Tuesday, September 15, 2015 - 6:45:33 AM

File

ASME_2006.pdf
Explicit agreement for this submission

Identifiers

  • HAL Id : hal-01154712, version 1

Collections

ENSTA | CNAM | ENSTA_UME | LMSSC-CNAM

Citation

M Amabili, Cyril Touzé, O Thomas. Comparison of Galerkin, POD and Nonlinear-Normal-Modes Models for Nonlinear Vibrations of Circular Cylindrical Shells. ASME IMECE 2006, International Mech. Engin. Congress and Exposition, 2006, Chicago, United States. ⟨hal-01154712⟩

Export

BibTeX TEI DC DCterms EndNote

Share

Metrics

Record views

217

Files downloads

243

Contact

Informations

CCSD